Mix of peanuts and cashews how many of each?

Question

Peanuts cost $7 a pound. Cashews costs 9$ a pound. There is a mixture of peanuts and cashews that weigh 10 pounds and costs$84.

Answer 1

Let x = pounds of peanuts

and 10 - x = pounds of cashews (10 - x because the total of both them is 10 pounds)

 

Adding the individual prices should be equal to the total of $84.

 

So it's the total price of peanuts plus total price of cashews equal to 84 or:

 

x*7 + (10-x)*9 = 84

7x + 90 - 9x = 84

 

-2x = -6

 

x = 3 ---> (10 - x) = 7

 

Therefore there 3 pounds of peanuts (x) and 7 pounds of cashews (10-x).

 

Answer 2

What we are looking for is weight of Peanuts (P) and Cashews (C).

 

What we know:

-10 lbs of peanuts and cashews in total

-The total cost is $84

 

From this we can create these equations:

P + C = 10    

7P + 9C = 84

⇒ Multiple the first equation by -7 (we do this so that the P's will cancel when we add the equations)

-7P - 7C = -70

7P + 9C = 84

⇒ Add the two equations together

2C = 14

⇒ Divide both sides by 2

C = 7

 

Returning to P + C = 10 we can plug in 7 for C and we find that P = 3.

3 lbs of Peanuts

7 lbs of Cashews

 

We can verify this is correct by plugging these values into each equation and making sure that they are equal.

 

Have a good day, hope this helped